Atomistic Description of Interdroplet Ice-Bridge Formation during Condensation Frosting.

The propagation of frost in an assembly of supercooled dew droplets takes place by the formation of ice protrusions that bridge ice particles and still-liquid droplets. In this work, we develop a Kinetic Monte Carlo (KMC) model to study the formation kinetics of the ice protrusions. The KMC simulations reproduce well the experimental results reported in the literature. The elongation speed of the ice protrusions does not depend on the droplet size but increases when the interdroplet distance decreases, the temperature increases, or the substrate wettability increases. While 2D diffusion of the water molecules on the substrate surface is sufficient to explain the process kinetics, high 3D (vapor) water-molecule concentration can lead to the development of 3D lateral branches on the ice protrusions. A 1D analytical model based on the water-molecule concentration gradient between a droplet and a nearby ice particle reproduces well the simulation results and highlights the relation between the protrusion elongation kinetics and parameters like the interdroplet distance, the water diffusivity, and the concentration gradient. The bridge-formation time has a quadratic dependence on the droplet-ice distance. Comparing the simulations, the analytical model, and the experimental results of the literature, we conclude that the propagation of frost on a flat substrate in an assembly of supercooled dew droplets with interdroplet spacing larger than about 1 µm is limited by water-molecule diffusivity.

Dynamics of Frost Propagation on Breath Figures.

We investigate the process of condensation frosting on flat surfaces using thermal imaging microscopy. This method is particularly well-suited to characterize the frosting of polydisperse assemblies of dew droplets, also called breath figures, that transform into ice droplets by the propagation of frost fronts. The front propagation speed is found to be a nonmonotonous function of the characteristic droplet size of the breath figure. In our experimental conditions, the propagation speed is maximum around 70 µm s-1 for a characteristic droplet radius of around 300 µm. We mainly show that the frost propagation speed is governed by the competition between two characteristic time scales. The first one is the freezing time of individual droplets, and the other one is the formation time of interdroplet ice bridges that grow from frozen to liquid droplets. In addition, the experiments reveal that the mean ice bridge speed is constant regardless of the characteristic radius of the liquid droplets in the breath figure. A theoretical mean-field analysis without any adjustable parameters recovers all of the features of the front propagation observed in experiments.